Question: Rewrite as a simplified fraction. ${0.9\overline{95} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 995.9595...\\ 10x &= 9.9595...\end{align*}}$ Subtracting the two equations, we have: ${990x = 986}$ ${x = \dfrac{986}{990}} $ ${x = \dfrac{493}{495}} $